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Dec 1998

Volume 66, Issue 12, pp. 1041-1126

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Answer to Question #65. What conditions determine crystal growth? The triangular ice spike

Charles A. Knight

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1041 | Cited 1 time

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01.50.-i Educational aids
64.70.D- Solid-liquid transitions
81.10.-h Methods of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation

Answer to Question #66. Why is the Hamiltonian of a magnetic dipole −m⋅B?

Daniel R. Stump

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1042

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41.60.-m Radiation by moving charges

Answer to Question #66. Why is the Hamiltonian of a magnetic dipole −m⋅B?

Ralph H. Young

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1043

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01.50.-i Educational aids
45.05.+x General theory of classical mechanics of discrete systems

Answer to Question #68. 60.000 Hz? Synchronization of the power grid

Robert H. Bushnell

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1044

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84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables

Answer to Question #76. Neutrino Mass and Helicity

Barry R. Holstein

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1045

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01.50.-i Educational aids
11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries
14.60.Lm Ordinary neutrinos
14.60.Pq Neutrino mass and mixing
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American Association of Physics Teachers 1998 Award for Excellence in Undergraduate Physics Teaching: John W. Jewett

Ronald D. Edge

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1046

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01.60.+q Biographies, tributes, personal notes, and obituaries

American Association of Physics Teachers 1998 Award for Excellence in Pre-College Physics Teaching: Robert Morse

Ronald D. Edge

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1047

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01.10.Cr Announcements, news, and awards
01.40.-d Education
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An advanced laboratory in nuclear-isotope mass spectroscopy

S. A. Shaheen, M. Shapiro, and F. D. Becchetti

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1048 | Cited 1 time

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We describe an experiment in nuclear-isotope mass spectroscopy, suitable for an advanced physics laboratory, which utilizes a relatively inexpensive commercial 60°-dipole residual gas analyzer. Students measure the terrestrial abundance of the isotope 22Ne relative to 20Ne and compare this with recent measurements of this ratio in meteorites. These ratios provide clues to the astrophysical sites, astrophysical processes, and nuclear reactions which formed these isotopes. The mass spectrometer is also used as a residual gas analyzer to examine the gas composition (O2, N2, H2O,…) at various pressures in a typical vacuum system. This gives students insight into the design of vacuum apparatus including the optimal selection of components such as vacuum pumps for particular applications. © 1998 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
32.10.Bi Atomic masses, mass spectra, abundances, and isotopes
98.80.Ft Origin, formation, and abundances of the elements
96.30.Za Meteors, meteorites and tektites

An experiment on electron wave–particle duality including a Planck constant measurement

G. Matteucci and C. Beeli

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1055

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An alternative approach with respect to the standard double-slit experiment is presented to introduce the wave-like behavior of electrons. This simple and pedagogical experiment requires a commercial transmission electron microscope and a ferromagnetic film transparent to electrons. It allows in addition the measurement of Planck’s constant. © 1998 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
06.20.Jr Determination of fundamental constants

Knots and physics: Old wine in new bottles

Allen C. Hirshfeld

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1060

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The history of the interplay between physics and mathematics in the theory of knots is briefly reviewed. In particular, Gauss’ original definition of the linking number in the context of electromagnetism is presented, along with analytical, algebraical, and geometrical derivations. In a modern context, the linking number appears in the first-order term in the perturbation expansion of a Wilson loop in Chern–Simons quantum field theory. New knot invariants, the Vassiliev numbers, arise in higher-order terms of the expansion, and can be written in a form which shows them to be generalizations of the linking number. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
02.40.Pc General topology
02.40.Re Algebraic topology
41.20.-q Applied classical electromagnetism
03.70.+k Theory of quantized fields
03.50.De Classical electromagnetism, Maxwell equations

Eddy current damping of a magnet moving through a pipe

Kenneth D. Hahn, Erik M. Johnson, Allen Brokken, and Steven Baldwin

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1066 | Cited 11 times

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A harmonic oscillator consisting of a neodymium magnet attached inside a spring is driven through resonance. Eddy currents, induced in pipes surrounding the magnet, result in a damping of the motion of the magnet. Our experiment makes precise measurements of the motion and damping of the magnet as we vary pipe composition, length, thickness, radius, and position. A theoretical analysis combining the standard differential equation for a damped, driven harmonic oscillator and Faraday’s law of electromagnetic induction gives excellent agreement with the experimental results. This analysis allows for the calculation of electromagnetic damping for any pipe configuration which is coaxial with the magnet’s motion and provides strong evidence for the eddy current damping analysis of the common demonstration of dropping a magnet down a conducting tube. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
07.55.Db Generation of magnetic fields; magnets
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Space–time intervals as light rectangles

N. David Mermin

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1077

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Two inertial observers in relative motion must each see the other’s clock running at the same rate. The representation of this symmetry of the Doppler effect in a two-dimensional space–time diagram reveals an important geometrical fact: The squared interval between two events is proportional to the area of the rectangle of photon lines with the events at diagonally opposite vertices. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

An ideal quantum gas in a finite-sized container

R. K. Pathria

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1080 | Cited 3 times

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The role of finite-size effects in determining the thermodynamic behavior of an ideal gas is critically examined. While classical statistics do not produce any perceptible effects, quantum statistics do yield results that play a crucial role in determining the low-temperature behavior of the given system. For illustration, we carry out an exact analysis of the ideal Bose gas in one dimension and show that at least in this case (i) the bulk term (customarily obtained by replacing the summation-over-states by an integration) yields results that are, at best, misleading, whereas (ii) the correct behavior of the system is determined almost entirely by terms representing finite-size effects. The subtle, yet distinctive, role played by the boundary conditions imposed on the system is also explored. © 1998 American Association of Physics Teachers.
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05.30.Jp Boson systems

Extensions of the Bohr–Sommerfeld formula to double-well potentials

L. V. Chebotarev

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1086

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Extensions of the Bohr–Sommerfeld quantization formula to smooth double wells are established which preserve the formula’s generality and simplicity as well as its accuracy and the ease of use. Moreover, the proposed quantization equations for double wells, while being free from the limitations of the Wentzel–Kramers–Brillouin approximation which is restricted to deep energy levels alone, are equally well suited for determining higher energy levels lying in the vicinity of the barrier’s top as well as above the latter, and they have the correct connection to the conventional Bohr–Sommerfeld formula as the particle’s energy becomes large enough. As a particular application, a simple quantization equation for the pure quartic oscillator is derived which yields correct energy eigenvalues for all eigenstates of the oscillator including the ground one, with relative errors being all less than 1%. Conditions for the validity of the extended quantization equations are discussed and their numerical verification is made. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

Triaxial bifurcations of rapidly rotating spheroids

Ts. Dankova and G. Rosensteel

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1095 | Cited 2 times

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A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The oblate and triaxial equilibrium configurations minimize the total energy, the sum of the rotational kinetic energy plus the potential energy. For a star or galaxy the potential is the self-gravitating potential, for a liquid drop, the surface tension energy, and for a nucleus, the potential is the sum of the repulsive Coulomb energy plus the attractive surface energy. A simple, but accurate, Padé approximation to the potential function is used for the energy minimization problem that permits closed analytic expressions to be derived. In particular, the critical deformation and angular velocity for bifurcation from MacLaurin spheroids to Jacobi ellipsoids is determined analytically in the approximation. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
05.45.-a Nonlinear dynamics and chaos
45.05.+x General theory of classical mechanics of discrete systems
47.55.D- Drops and bubbles
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
97.10.Kc Stellar rotation

Regularization and renormalization in scattering from Dirac delta potentials

Indrajit Mitra, Ananda DasGupta, and Binayak Dutta-Roy

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1101 | Cited 7 times

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Various regularization schemes used in quantum field theory, including the widely used dimensional regularization scheme, and the concept of renormalization, are introduced through the study of scattering from an attractive Dirac delta potential in more than one dimension. This is expected to make such advanced concepts and techniques available to enthusiastic beginners within the realm of elementary quantum mechanics. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Fd Algebraic methods
03.70.+k Theory of quantized fields

Newtonian jerky dynamics: Some general properties

Stefan J. Linz

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1109 | Cited 1 time

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We clarify and generalize the recently introduced concept of a Newtonian jerky dynamics. We also discuss several analytically accessible properties of these systems, including their general functional form, periodic solutions and conserved quantities, symmetries, and nonchaotic behavior.© 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
05.45.-a Nonlinear dynamics and chaos
45.05.+x General theory of classical mechanics of discrete systems

Angle states in quantum mechanics

A. C. de la Torre and J. L. Iguain

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1115

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Angle states and angle operators are defined for a system with arbitrary angular momentum. They provide a reasonable formalization of the concept of angle provided that we accept that the angular orientation is quantized. The angle operator is the generator of boosts in angular momentum and is, almost everywhere, linearly related to the logarithm of the shift operator. Angle states for fermions and bosons behave differently under parity transformation. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory

Attempt frequency in tunneling

Peter J. Price

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1119 | Cited 2 times

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The nature of the “attempt frequency,” in the rate of escape of a particle from a confining structure by quantum tunneling through its outer barrier, is elucidated. It is shown that even for a general internal potential the reciprocal of the attempt frequency is equal to the formal quantum propagation time that is given by the energy derivative of the “round trip” phase change for the wave function reflected from and returning to the barrier. © 1998 American Association of Physics Teachers.
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01.50.-i Educational aids
73.40.Gk Tunneling
03.65.-w Quantum mechanics
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Quantitative measurements of the acoustic Doppler effect using a walking speed source

A. J. Cox and Joel J. Peavy

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1123 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
43.28.Bj Mechanisms affecting sound propagation in air, sound speed in the air

Comment on “Variations on the Aharonov–Bohm effect” [Am. J. Phys. 59 (12), 1080–1085 (1991)]

S. Bruce

American Journal of Physics -- December 1998 -- Volume 66, Issue 12, pp. 1125 | Cited 2 times

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Abstract Unavailable
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory
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